Washington
— While political dust storms begin to swirl around President Reagan's new budget, experts across a broad spectrum are arguing with the budget's economic logic.

''The deficits,'' says Herbert Stein, chief economic adviser to President Nixon and now with the American Enterprise Institute (AEI), ''are going to be substantially larger than President Reagan projects.''

A basic problem, as a number of critical economists see it, is that nothing in the President's '83 budget will keep deficits from climbing--even if the economy recovers and begins to grow.

Government outlays, by contrast, according to the Congressional Budget Office (CBO), will remain constant at about 23 percent of GNP. This would push the deficit from 2 percent of GNP in 1981 to roughly 5 percent in 1987.

''Even under relatively optimistic assumptions,'' says CBO director Alice M. Rivlin, ''deficits will rise very quickly. What is worrying is when deficits grow in an expanding economy, a recovery period. Then those deficits must be financed (by government borrowing) at a time of rising private demand for capital.''

The White House responds that the deficit as well as private borrowing needs can both be funded with the help of higher private savings. The government projects that lower taxes and special measures to encourage savings will turn the American people into a nation of savers.

White House officials also dispute the forecast that future deficits will rise. They argue that prosperity will generate fresh tax revenues and that Americans will save more than they have in the past. From these twin pools of taxes and savings, says Treasury Secretary Donald T. Regan, enough revenue will come to reduce future budget deficits.

Dr. Stein, who doubts the White House forecast of savings, says:

''Historically, the savings rate of the private sector is 16 percent of GNP-- 5 or 6 percent from individuals, 10 to 11 percent from corporations.

''To finance a deficit that is, even at the most optimistic, 2 percent of GNP ,'' he says, ''you would need about a 40 percent increase in the individual savings rate.

William Fellner, resident scholar of the AEI, finds an incompatibility between the economic growth rate expected by the Reagan administration and the continuing fight against inflation.

''The Reagan budget,'' says Dr. Fellner, ''is based on a 10 percent nominal growth of the economy. Historically, this kind of growth always has been inflationary. So it is hard to see how the administration can expect to reduce inflation on the basis of the growth they expect.''

Will the White House, asks Dr. Stein, put pressure on the Federal Reserve Board to expand the money supply to accommodate both public and private demand for capital in an effort to prod the economy?

This, in his view and that of Dr. Fellner, would be inflationary. Conversely, if the Fed maintains a tight policy to combat inflation, interest rates may shoot upwards.

''The Reagan 1983 budget,'' says AEI economist Rudolph Penner, ''does not include a margin of error. That is, the Ford budget of 1976 and the Carter budget of 1981 looked forward to (the possibility of) surplus budgets.

''But,'' says Dr. Penner, director of AEI's Fiscal Policy Studies Program, ''the Reagan projection has no surplus budget in sight.'' This makes more critical the accuracy of White House projections.

Boiled down, the concerns of economists quoted above come down to this:

* The huge tax cuts stretching out through 1984, to be followed by indexation of tax rates for inflation, drain the government of too much money to pay its bills.

* No evidence from the past indicates that massive tax cuts will generate enough new savings, investment, and tax payments to offset this drain.

* If, under these circumstances, the economy grows briskly, the Federal Reserve Board will confront a dilemma--either to ''print more money'' (i.e., expand the money supply) and risk renewed inflation, or watch interest rates climb due to tight money.

* President Reagan shows no readiness to take major corrective steps, such as cutting back on Social Security, reducing the huge defense increase, or raising taxes.

The White House counters, in brief: 1. Tax cuts will boost output, and eventually tax revenues, to pay the government's bills; 2. Savings can be stimulated through lower taxes and liberalized savings programs; 3. A moderate increase in money supply will finance expansion without rekindling inflation; 4. The President's program - now just over four months old--must be given time to work.